HI,
Let a,b be two unit vectors whose sum is also a unit vector c
a+b=c ...... (i) and |a|=|b|=|c|=1
Now, magnitude of sum of a and b is
|a+b|=|a|^2+|b|^2+2(a⋅b)
1=1+1+2(a⋅b) ..... From (i)
a⋅b=−1/2
Magnitude of their difference is given by
|a−b|^2=|a|^2+|b|^2−2a.b
=1+1+2×21=3
|a−b|=root (3)
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